Chapter 5 Loops

Motivations Suppose that you need to print a string (e.g., "Programming is fun!") a hundred times. It would be tedious to have to write the following statement a hundred times: print("Programming is fun!"); So, how do you solve this problem?

Opening Problem Problem: print("Programming is fun!"); … 100 times

Objectives To write programs for executing statements repeatedly by using a while loop (§5.2). To develop loops following the loop design strategy (§§5.2.1-5.2.3). To control a loop with the user’s confirmation (§5.2.4). To control a loop with a sentinel value (§5.2.5). To obtain a large amount of input from a file by using input redirection instead of typing from the keyboard (§5.2.6). To use for loops to implement counter-controlled loops (§5.3). To write nested loops (§5.4). To learn the techniques for minimizing numerical errors (§5.5). To learn loops from a variety of examples (GCD, FutureTuition, MonteCarloSimulation, PrimeNumber) (§§5.6, 5.8). To implement program control with break and continue (§5.7). To use a loop to control and simulate a random walk (§5.9).

Introducing while Loops count = 0 while count < 100: print("Programming is fun!") count = count + 1

while Loop Flow Chart count = 0 while count < 100: print("Programming is fun!") count = count + 1 while loop-continuation-condition: # Loop body Statement(s)

Trace while Loop count = 0 while count < 2: animation Trace while Loop Initialize count count = 0 while count < 2: print("Programming is fun!") count = count + 1

Trace while Loop, cont. count = 0 while count < 2: animation Trace while Loop, cont. (count < 2) is true count = 0 while count < 2: print("Programming is fun!") count = count + 1

Print Welcome to Python animation Trace while Loop, cont. Print Welcome to Python count = 0 while count < 2: print("Programming is fun!") count = count + 1

Trace while Loop, cont. count = 0 while count < 2: animation Trace while Loop, cont. Increase count by 1 count is 1 now count = 0 while count < 2: print("Programming is fun!") count = count + 1

(count < 2) is still true since count is 1 animation Trace while Loop, cont. (count < 2) is still true since count is 1 count = 0 while count < 2: print("Programming is fun!") count = count + 1

Print Welcome to Python animation Trace while Loop, cont. Print Welcome to Python count = 0 while count < 2: print("Programming is fun!") count = count + 1

Trace while Loop, cont. count = 0 while count < 2: animation Trace while Loop, cont. Increase count by 1 count is 2 now count = 0 while count < 2: print("Programming is fun!") count = count + 1

(count < 2) is false since count is 2 now animation Trace while Loop, cont. (count < 2) is false since count is 2 now count = 0 while count < 2: print("Programming is fun!") count = count + 1

The loop exits. Execute the next statement after the loop. animation Trace while Loop The loop exits. Execute the next statement after the loop. count = 0 while count < 2: print("Programming is fun!") count = count + 1

Problem: Guessing Numbers Write a program that randomly generates an integer between 0 and 100, inclusive. The program prompts the user to enter a number continuously until the number matches the randomly generated number. For each user input, the program tells the user whether the input is too low or too high, so the user can choose the next input intelligently. Here is a sample run: GuestNumberOneTime GuessNumber Run

Problem: An Advanced Math Learning Tool The Math subtraction learning tool program generates just one question for each run. You can use a loop to generate questions repeatedly. This example gives a program that generates five questions and reports the number of the correct answers after a student answers all five questions. SubtractionQuizLoop Run

Ending a Loop with a Sentinel Value Often the number of times a loop is executed is not predetermined. You may use an input value to signify the end of the loop. Such a value is known as a sentinel value. Write a program that reads and calculates the sum of an unspecified number of integers. The input 0 signifies the end of the input. SentinelValue Run

Caution Don’t use floating-point values for equality checking in a loop control. Since floating- point values are approximations for some values, using them could result in imprecise counter values and inaccurate results. Consider the following code for computing 1 + 0.9 + 0.8 + ... + 0.1: item = 1 sum = 0 while item != 0: # No guarantee item will be 0 sum += item item -= 0.1 print(sum) Variable item starts with 1 and is reduced by 0.1 every time the loop body is executed. The loop should terminate when item becomes 0. However, there is no guarantee that item will be exactly 0, because the floating-point arithmetic is approximated. This loop seems OK on the surface, but it is actually an infinite loop. InfiniteLoop Run

for Loops for i in range(initialValue, endValue): # Loop body i = initialValue # Initialize loop-control variable while i < endValue: # Loop body ... i++ # Adjust loop-control variable for i in range(initialValue, endValue): # Loop body

range(a, b) >>> for v in range(4, 8): ... print(v) ... 4 5 6 7 >>>

>>> for i in range(4): ... print(i) ... 0 1 2 3 >>> range(b) >>> for i in range(4): ... print(i) ... 0 1 2 3 >>>

range(a, b, step) >>> for v in range(3, 9, 2): ... print(v) ... 3 5 7 >>>

>>> for v in range(5, 1, -1): ... print(v) ... 5 4 3 2 range(a, b, step) >>> for v in range(5, 1, -1): ... print(v) ... 5 4 3 2 >>> Note: The numbers in the range function must be integers.

Nested Loops Problem: Write a program that uses nested for loops to print a multiplication table. MultiplicationTable Run

NestedLoopTime 26 Run

Minimizing Numerical Errors Numeric errors involving floating-point numbers are inevitable. This section discusses how to minimize such errors through an example. Here is an example that sums a series that starts with 0.01 and ends with 1.0. The numbers in the series will increment by 0.01, as follows: 0.01 + 0.02 + 0.03 and so on. TestSum Run

After this loop, sum = 50.5 28

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Problem: Finding the Greatest Common Divisor Problem: Write a program that prompts the user to enter two positive integers and finds their greatest common divisor. Solution: Suppose you enter two integers 4 and 2, their greatest common divisor is 2. Suppose you enter two integers 16 and 24, their greatest common divisor is 8. So, how do you find the greatest common divisor? Let the two input integers be n1 and n2. You know number 1 is a common divisor, but it may not be the greatest commons divisor. So you can check whether k (for k = 2, 3, 4, and so on) is a common divisor for n1 and n2, until k is greater than n1 or n2. GreatestCommonDivisor Run

It does not include n1 or n2 as a possible divisor 31

Problem: Predicting the Future Tuition Problem: Suppose that the tuition for a university is $10,000 this year and tuition increases 7% every year. In how many years will the tuition be doubled? FutureTuition Run

Using break and continue Examples for using the break and continue keywords: TestBreak TestContinue Run

break

continue

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Guessing Number Problem Revisited Here is a program for guessing a number. You can rewrite it using a break statement. GuessNumberUsingBreak Run

Problem: Displaying Prime Numbers Problem: Write a program that displays the first 50 prime numbers in five lines, each of which contains 10 numbers. An integer greater than 1 is prime if its only positive divisor is 1 or itself. For example, 2, 3, 5, and 7 are prime numbers, but 4, 6, 8, and 9 are not. Solution: The problem can be broken into the following tasks: For number = 2, 3, 4, 5, 6, ..., test whether the number is prime. Count the prime numbers. Print each prime number, and print 10 numbers per line.

Algorithm for the Problem PrimeNumber 40 Run

Turtle: Random Walk RandomWalk Run